The simple flaw in Marx's work as far as I can tell is treating price as a single thing and then using that as the basis for exchange value. The price paid for something can vary wildly from any given sticker price and so you can't establish exchange value without some stability.
Specifically, the sticker price has to be a reliable indicator of a clearing price ("no free lunch") or else it's not actually an evaluation but just some nebulous signpost. In that case, there's one single price because anything else is arbitraged away, otherwise there's not.
But for such a clearing price to exist, the market needs to be highly liquid such that there's a certain uniformity and frequency of transactions. The creation of such liquid markets is inextricable from the phenomenon of industrialization, which enabled such a thing by engendering a material economy built on and around interchangeable parts. This kind of economy is a prerequisite for any kind of labor theory of value insofar that a clearing price can be found for some kind of interchangeable, and therefore measurable, output of a rote task by a laborer.
It's possible that Marx understood this on some level insofar that he seems to understand capitalism (and by extension the "value form") as a pattern of mechanization and rationalization where the possibility of monetary profit is made tractable by reducing workers to sufficiently rote tasks and in the process making them replaceable by relatively simple servomechanisms in the future.
This pattern grows insofar as it systematizes more and more things and in doing so reduces human efforts to measurable outfits that can be arbitraged until competition brings things down to a clearing price, eventually bringing about an ossified cybernetic system that can only grow by grabbing more unmapped territory and repeating the process all over again.